I guess I’ll try my hand at this 🙂
The density of the overall network is seemingly high which reflects a good deal of interactions between the actors (assuming the ties stand for mentions/replies/retweets).
Your following network shows that you are interested in 3 distinct subjects since there are 3 clusters or subgroups (Each probably gathered around a common interest: digital media and social change -red- Media anthropology -green- and democracy -blue-).
Some tweeps “Hubs” are very influential within these subgroups (referred to by the size of the node: Clay Shirky for the red cluster for instance). But there are also interesting profiles such as Gabriella Coleman who lies at the intersection of the 3 clusters and plays a “connector” role in the network (he bridges the distinct subgroups).
That’s what I could gather from the image so far, I’d love to see how right this succinct analysis is!

Thanks for posting the graph. Let me tell you a little bit more about it. @Lamia is pretty close on a lot of it – of course it is impossible to interpret it perfectly without knowing what data and algorithms I used.
The network: is comprised of John’s followers (ego network) with the node representing him removed. So, there is an implicit between each of the nodes here and John.

The links: represent follow relationships. These relationships are directed rather then necessarily reciprocal and the links have arrows indicating that (although the picture may be too small to see them).

The nodes: are weighted (displayed as size) according to “in degree” which means that the largest of them is followed by the most people that you follow. We can interpret this *roughly* as people you want to hear from tend to want to hear from the large nodes. This *was not* normalized for anything like total number of followers, so people with more followers in general would tend to have more followers here as well and thus might not be a unique characteristic of your network.

Color represents communities as determined by a standard community detection algorithm – from a paper by Blondel, Guillaume et al (2008) (http://arxiv.org/abs/0803.0476). Results vary slightly each time you run it because it starts with some randomized parameters.

Finally, the graph is layed out using a force directed algorithm – uses a physical model of gravity of nodes and springs to arrange things. It is an in house algorithm from the platform I was using – great open source software called Gephi: http://gephi.org/tag/algorithm/

Finally, a few stats: The diameter is 7 (longest path between any two nodes). The density is .074, which means about 7 percent of all possible links if everybody followed everyone else are there. This is a fairly high density for a twitter graph I think. The average link between any two nodes is 2.6.

Excellent stuff, many thanks for the explanation, Alexander!. Are you doing any more of these graphs? It’d be interesting to compare other people’s.

So what can this kind of approach tell us about Twitter-mediated social relations? Like most social anthropologists (I guess), I never quite know what to do with social network analysis. How do these graphs fit into your own research activities?

I am doing more of these graphs, yes. I would be happy to share some with you.
I understand your skepticism about these graphs (in terms of what they can *actually* tell us) – often times they are more flashy than informative. The graph I made here may fall into that category. It is hard for them to tell us much of anything without a baseline comparison to see which features (density, clustering etc.) are significant and unusual.
In terms of my own research, I am collecting a large group of ego networks like this and collecting a large set of tweets from each ego and alter in the network. I am using Latent Semantic Analysis to see how semantically similar the content of what people tweet is to what those they follow tweet. I am then regressing this semantic similarity metric against various traits of the users network and the user. Essentially, are people with much more densely connected networks more likely to tweet things that are very semantically similar to people in their network etc. It is a way of trying to measure echo-chamber effects.